Orbital shrinking: Theory and applications

We present a method, based on formulation symmetry, for generating Mixed-Integer Linear Programming (MILP) relaxations with fewer variables than the original symmetric MILP. Our technique also extends to convex MINLP, and some nonconvex MINLP with a special structure. We showcase the effectiveness of our relaxation when embedded in a decomposition method applied to two important applications (multi-activity shift scheduling and multiple knapsack problem), showing that it can improve CPU times by several orders of magnitude compared to pure MIP or CP approaches.